When Charles Dodgson, the author of so many weighty treatises on Euclid and determinants and plane trigonometry, blossomed out into the brilliant writer of fantasy, Lewis Carroll, he gave the lie to the prevalent conception of the mathematician as a dull and unimaginative creature. To a fertile imagination, in fact, the science of mathematics, in its boundless scope, must afford a fascinating and almost irresistible attraction, for it has a bearing upon every other science and, in some form, every art too. Its bearing on the art of ballet is apparent from the first view of a choreographer's dispositions. It would certainly be interesting to know how well versed in mathematics are our choreographers of today; but it would be even more interesting if a prominent mathematician showed an aptitude for choreography, and were permitted to enrich the repertory with a ballet of his own composing.

Such an eventuality might have come to pass about a hundred years ago, had not Mr Benjamin Lumley, the director of her Majesty's Theatre, London, had prudent fears for the safety of his house and his audiences. The mathematician in question was Charles Babbage, known today for his pioneer work in the construction of calculating machines: his unfinished 'analytical engine', a magnificent inachievemnet, is now to be seen at the Science Museum in South Kensington. Like many another genius, Babbage was eccentric. he had a particular aversion to street music in all its forms - barrel-organs, brass bands, bagpipes, halfpenny whistles; in fact, every source of cacophony he could hear from his study window - and throughout his life he carried on a furious crusade to have these nuisances banished from the streets of London by force of law. So persistent were his efforts in this direction that he became the butt of his neighbours, whom he accused of bribing German bands to play outside his house and sending little urchins to jeer at him in the streets. He summed up the harm done him by these annoyances in the following words: 'On a careful retrospect of the last dozen years of my life,' he wrote, 'I have arrived at the conclusion that I speak within the limit when I state that one-fourth part of my working power has been destroyed by the nuisance against which I have protested.'

Mr Babbage's inspiration came to him while watching a performance of Meyerbeer's Robert the Devil, probably the production of that opera in German, given at the Theatre Royal, Drury Lane, in the summer of 1841. During the ballet of the ghostly nuns in the moonlit cloister, he observed that the bonnet of the lady by his side and indeed every white object near him had assumed a pinkish hue. This contrast of colour led him to ponder over the effects that might be obtained by the use of coloured lights playing on the white dresses on the danseuses, and shortly afterwards he began making experiments in his laboratory to this end.*

He soon reached the conclusion that coloured light could be produced by two methods: by transmitting a strong light through a coloured medium, either fluid, as through a solution of indigo, or solid, as through coloured glass; and by making the source of light itself coloured, as by putting chemical salts in the wick of a spirits-of-wine lamp or by burning certain metallic oxides in an oxyhydrogen flame. He made many experiments by filling cells formed by pieces of parallel plate galss with solutions of various salts: potassium bichromate to produce yellow or orange light, according to the strength of the soloution, a solution of gum in suphuric acid to produce green light, and so on.

He realized that a more intense light would be needed for his purpose than that given out by gas light, which was then the universal mode of stage lighting, for much of the brilliancy of the light source would be absorbed in the the coloured meduim through which it had to pass. Drummond lighting - or more popularly, limelight - seemed most suitable to his purpose. This form of lighting, the principle of which was the raising of lime to a high temperature by means of an oxyhydrogen flame, had been invented in 1816, and, because of its brilliancy, was used for spotlights. An alternative method was offered by electricity, but this was still very much in its infancy, and had not up to then been used for theatrical purposes.**

The effects that Babbage obtained in his experiments were so superb that he at once devised a dance in which they could be exhibited, and which he entitled the 'Rainbow Dance'. He proposed to dispense with the footlights, and to substitute for them four 'urns with flowers', each of which would conceal from the audience an intense light of some colour. Their rays would be projected towards the back of the stage, forming four cones of various colours. The accompanying diagram, copied from Babbage's notes preserved in the Manuscript Department of the British Museum, illustrates the efffects he hoped to obtain from his 'Rainbow Dance', which he described at length in his memoirs, Passages from the Life of a Philosopher (London, 1864).

'Four groups,' he wrote, 'each of fifteen danseuses in pure white, would now enter on the stage. Each group would assume the colour of the light in which it was placed. Thus four dances each of a different colour would commence. Occasionally a damsel from a group of one colour would spring into another group, thus resembling a shooting star. After a time, the coloured lights would expand laterally and overlap each other, thus producing all the colours of the rainbow. In the meantime the sixty damsels in pure white forming one vast ellipse, would dance round, each in turn assuming, as it passed through them, all the prismatic colours.'

Lighting Plan for Charles Babbage's Rainbow Dance. The four dotted circles denote the four groups of 15 danseuses, each dancing in a different cone of light. The dotted ellipse at the back represents the whole corps de ballet, dancing in every colour of the rainbow.

One of Babbage's friends, who knew of these experiments, spoke of them to Mr Benjamin Lumley, the lessee of Her Majesty's Theatre, then the Italian Opera House. Lumley was very proud of his ballet, which at some time or other had featured nearly all of the great Continental ballerine, and he at once saw the novel possibilites that Babbage's idea offered. Consequently, some time early in 1845, a series of experiments was arranged to take place before him. Large sheets of patent net of varying shapes and sizes were suspended from ropes stretching across a concert hall, and were displayed in coloured lights of every conceivable hue: bright blues, brilliant greens, fiery reds, and, in particular, 'an almost perfect resemblance of the dead purple powdery coating of the finest grapes'.

Further inspired by the success of these experiments, Babbage became still more ambitious and even thought of writing a story to indroduce his 'Rainbow Dance', and 'to give it a moral character'. Thus was born, to use Babbage's own description, 'the beautiful ballet of Alethes and Iris'.#

The ballet was divided into six scenes.

The first scene is set in the deepest and most sacred portion of the Temple of the Sun, where Alethes, the priest of the Sun, feels that life is sad without a companion to share it. He makes a magnificent sacrifice to his god, and prays for his desire to be gratified. Thereupon, in the midst of clouds and incense, he falls into a trance and beholds in a vision a distant point of light coming nearer and nearer until it becomes a circular rainbow from which emerges 'a form of beauty more resplendant than mortal eyes might bear'. She approaches the Book of Fate that lies closed on a golden pedestal, opens it, and inscribes in purple sybmols some mystic signs. Then she waves her arm gracefully over the spellbound Alethes, and vanishes as she had appeared. Alethes, recovering from his trance, rushes over to the Book of Fate and from its pages learns 'that, with constancy and perseverence through danger, he may find in a distant sphere a spirit worthy of his love, and that he may give to her renewed life'.

In the second scene, Alethes has descended into a glacier to search the frozen waters for the object of his love. A spectacular diarama exhibits 'all the inhabitants of the ocean, comprising big fishes, lobsters, and various crustacea, mollusca, coralines, etc.' Then follows the Dance of the Frozen, a slow, gliding dance, performed by the Gnomes of the Ice and Alethes, after which the scene ends with the apparition of Iris in a vision. (Babbage's notes show that, in his original conception of this scene, he had considered the use of skates and artificial ice.)

The third scene opens to show the Antarctic regions. 'An active volcano and a river of boiling water, supplied by geysers cutting their way through cliffs of blue ice' transform the ice into fiery rocks, an effect to be obtained by varying the colours of the lighting. Then 'Gnomes of Fire appear, and the Fire Dance on red-hot lava is joined by Alethes. The gnomes disappear. The vision of Iris reappears, and Alethes gradually falls asleep whilst the fires cool amidst slow music.'

As the curtain rises on the fourth scene, Alethes is awakening from his sleep in a white marble palace. At the back of the stage is a tomb on which a beautiful girl is reclining on black velvet cushions. Alethes sees her, and with his magic powers revives her. 'Pale blue light having been thrown upon her white dress, she appears dead,' read Babbage's instructions, 'but the blue gradually being turned off and pink light as gradually turned on, she gradually becomes warmed with life.' Alethes then repectfully raises her, she descends from the marble, and they dance, the marble palace having become also coloured.

The Rainbow Dance is introduced in to the fifth scene, being danced by Alethes and Iris and their attendant nymphs.

In the sixth and final scene, Alethes, and Iris and the nymphs enter again. The nymphs eventually retire and then reappear in a circular rainbow that begins as a tiny point of light, then enlarges and opens out, finally contracting into a point of light again. As Alethes and Iris descend to earth, a diorama shows 'the animals whose various remains are contained in each successive layer of the earth's crust. In the lower portions symptoms of the increasing heat show themselves until the centre is reached, which contains a liquid transparent sea, consisisting of some fluid at white heat, which, however, is filled up with little infinitesimal eels, all of one sort, wriggling eternally.'

Such was Babbage's ballet. When he was describing it in his memoirs, he felt that some explanation was necessary, for he was living in the prosaic Victorian age. 'This would have produced a magnificent spectacle considered merely as a show,' he wrote, 'but the moralist might, if he pleased, have discovered in it a profound philosophy. The ennui and lassitude felt by the priest of the Sun arose from the want of occupation for his powerful mind. The remedy proposed in the ballet was - look into all the works of creation. The central ocean of frying eels was added to assist the teaching of those ministers who prefer the doctrine of the eternity of bodily torment.'

After Babbage had consulted with the chef de ballet ## as to the nature of the steps, his Rainbow Dance was performed before Lumley. Babbage had been supplied with the dimensions of the theatre, and had installed several powerful limelights emitting red, yellow, blue and purple light respectively. Lumley was very apprehensive of the danger of fire from the use of limelight, and had taken the precaution of ordering two fire engines, which were duly placed on the stage under the supervison of a section of the fire brigade.

The experiment was very successful and shrotly afterwards Lumley wrote to Babbage: 'Whatever you may think necessary shall be ordered. I hope it progresses to your satisfaction. I was much gratified with the experiments and have to thank you for the idea, and for all the trouble you are taking in the affair.' (February 2nd, 1846.)

The danger from fire remained the main obstacle to staging the ballet. Lumley had been greatly impressed by the brilliancy of the colours and the effect of the Rainbow Dance, but prudently hesitated to make a decision that, in his opinion, might involove the destruction of his theatre. Babbage tried to reassure him, and, to show that he apprehended no such danger himself, even offered to be present in the house at every performance, but to this Lumley pointed out that if the theatre were burnt, his customers would be burnt with it, which, Babbage allowed, 'was certainly a valid objection for though he could have insured the building, he could not have insured his audience.'

And with that philosophical reflection, Babbage turned his back on the ballet and returned to his first love, the analytical engine. Fortunately he was a methodical man, for he carefully kept all his correspondence and notes, which have enabled the story of his ballet to be recorded here in detail for the first time. Had it not been for Lumley's fear of fire, this ballet would doubtless have beeen performed at Her Majesty's Theatre in 1846 or1847, and might well have earned an honourable place in the annals of the theatre for being the first work in which coloured lighting was scientifically employed on the stage.

* Babbage was not the only person to be inspired by this scene. It inspired the tenor, Adolphe Nourrit, to write the scenario of La Sylphide, and also the artist, Degas, whose impression of it, painted in oils in 1872, can be seen at the Victoria and Albert Museum.

** Electric lighting made its first appearance in a theatre at the Paris Opéra in 1849, when the effect of a rising sun in Act III of Meyerbeer's opera, Le Prophète, was obtained by means of a carbon arc, supplied by a large electric battery consisting of some fifty elements. Although causing quite a sensation at the time for its brilliancy, it was only used very rarely owing to the expense of charging and maintaining the battery, and did not come into general use in the theatre until later in the century, when the incandescent lamp had been invented. The Paris Opéra was once again first in the field, electricity being installed there in 1881; the Savoy Theatre, London, changed from gas to electricity the following year.

# The description of this ballet that follows is based partly on the account of it in Babbage's memoirs (op. cit.), and partly on his manuscript notes in the British Museum (Addn. MSS 37193 ff. 195-204, 212-3, 236, 250, 254, 256).

## Babbage describes him thus in his memoirs. The person referred to might have been Gosselin, the Assistant Ballet Master, or Bertrand, the Regisseur.